Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problema 38a

Capitolo 3, Problema 38a

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3| a. f(5)

Guida verificata passo dopo passo

Step 1: Understand the function f(x) = |x + 3| / |x + 3|. This function involves absolute values in both the numerator and denominator. The absolute value of a number is its distance from zero, so it is always non-negative.

Step 2: Substitute the given value of x = 5 into the function. This means replacing x with 5 in both the numerator and denominator: f(5) = |5 + 3| / |5 + 3|.

Step 3: Simplify the expression inside the absolute value symbols. Calculate 5 + 3, which equals 8. So the function becomes f(5) = |8| / |8|.

Step 4: Evaluate the absolute values. Since 8 is already positive, |8| = 8. Therefore, the function simplifies to f(5) = 8 / 8.

Step 5: Simplify the fraction. Divide the numerator by the denominator: 8 / 8 simplifies to 1. Thus, the value of f(5) is 1.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Absolute Value Function

The absolute value function, denoted as |x|, represents the distance of a number x from zero on the number line, always yielding a non-negative result. For example, |5| equals 5, while |-5| also equals 5. This function is crucial in evaluating expressions that involve both positive and negative values.

Video consigliato:

4:56

Function Composition

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function to determine the corresponding output. In this case, evaluating f(5) means replacing x with 5 in the function f(x) = |x + 3| / |x + 3|, which simplifies the process of finding the function's value at that point.

Video consigliato:

4:26

Evaluating Composed Functions

Simplification of Rational Expressions

Simplification of rational expressions involves reducing fractions to their simplest form by canceling common factors in the numerator and denominator. In the given function, |x + 3| appears in both the numerator and denominator, which can lead to simplification, provided that the denominator is not zero, ensuring the expression remains valid.

Video consigliato:

02:58

Rationalizing Denominators

Pratica correlata

Domanda del libro di testo

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3| b. f(-5)

217

views

Domanda del libro di testo

Find f/g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15

914

views

Domanda del libro di testo

In Exercises 37–40, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-1, -2) and (-3, -4)

159

views

Domanda del libro di testo

Evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/(x + 3) c. f(−9 - x)

151

views

Domanda del libro di testo

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ . Determine the domain for each function.

$f$\left$(x$\right$)=5-x^2$ , $g$\left$(x$\right$)=x^2+4x-12$

626

views

Domanda del libro di testo

Write the standard form of the equation of the circle with the given center and radius. Center (-4, 0), r = 10

851

views